The Lady Claire was captured in Castlegard when she led the time travel team there, but Marek freed her and delivered her safely to her brother Lord Arnaut’s armies across the river. Marek winds up with mixed feelings, when on the one hand he thought he damaged history by saving her and on the other hand he sees her again captive on the wall of Castle La Roque. Professor Johnston tells him it was inevitable, because it is history. Marek then determines to change history.
The professor is mistaken; it is nothing so dramatic as an immutable past. It is instead a simple matter of not understanding the events in the original history and confusing their own changes with the causes of those events.
We are not certain where Claire was prior to her first interaction with the time travelers, when she yelled (in French) that they should run and hide, and Marek wound up crawling into her hiding place alongside her. However, it seems she had been missing for a significant time and was attempting to get back to her brother Arnaut without being caught by the English. Lord Oliver later suggests that Arnaut used his own sister as a spy, and it may be that this is what she was doing. At Marek’s request, after he apparently saves her at the risk of his own life, she agrees to take him and his friends to Castlegard. There she is captured, and we are fooled into thinking that this is the cause of her having been in English custody during the battle.
It is important to consider what would have happened had Marek not intervened. Claire had escaped her English pursuers and secured a hiding place near the river. She would not have been found before the French raiding party put an arrow in one of the English knights, diverting her pursuers in another chase. From there she undoubtedly would have crossed the river and reunited with her brother’s forces several hours earlier than she does in the film–but she would then have stayed with them for the remainder of the day. It is Arnaut’s intention to attack that night, and the English spy will still overhear this and report their position to the English command, who will raid the army at much the same moment. Claire will flee and be captured as she is in the film. The difference is after the time travelers intervene she is captured twice that day. They have nothing to do with the second incarceration, which was the only captivity in the original history, and the one that put her on the wall at the critical moment.
Thus the professor was mistaken. In fact, they can change history, and they did change history–they just didn’t happen to change the part of history they thought they did.